Fine frequency offset estimation and calculation and use to improve communication system performance

ABSTRACT

A method for correcting influence of frequency offset between a receiver and a transmitter by evaluating training symbols received during a preamble period. The method includes producing, based on at least one long training symbol, a first vector whose first vector angle is indicative of a fine offset between the receiver and the transmitter, producing a fine offset estimate based on the first vector angle, and multiplying, with a signal having a frequency based upon the fine offset estimate, data symbols that are received after the at least one long training symbol is received.

FIELD

The present invention pertains generally to automatic frequency control.More particularly, the present invention relates to supplementing acoarse frequency estimate with a fine frequency estimate derived frommore data than the coarse frequency estimate and using the finefrequency estimate to improve a communication system's performance.

BACKGROUND

The market for home networking is developing at a phenomenal rate.Service providers from cable television, telephony and digitalsubscriber line markets are vying to deliver bundled services such asbasic telephone service, Internet access and entertainment directly tothe consumer. Collectively these services require a high-bandwidthnetwork that can deliver 30 Mbits/s or even higher rates. The Instituteof Electrical and Electronic Engineers (IEEE) 802.11a standard describesa cost-effective, robust, high-performance local-area network (LAN)technology for distributing this multimedia information within the home.Networks that will operate in accordance with standard 802.11a will usethe 5-GHz UNII (unlicensed National Information Infrastructure) band andmay achieve data rates as high as 54 Mbits/s, a significant improvementover other standards-based wireless technology. The 802.11a standard hassome unique and distinct advantages over other wireless standards inthat it uses orthogonal frequency-division multiplexing (OFDM) asopposed to spread spectrum, and it operates in the clean band offrequencies at 5 GHz.

OFDM is a technology that resolves many of the problems associated withthe indoor wireless environment. Indoor environments such as homes andoffices are difficult because the radio system has to deal with aphenomenon called “multipath.” Multipath is the effect of multiplereceived radio signals coming from reflections off walls, ceilings,floors, furniture, people and other objects. In addition, the radio hasto deal with another frequency phenomenon called “fading,” whereblockage of the signal occurs due to objects or the position of acommunications device (e.g., telephone, TV) relative to the transceiverthat gives the device access to the cables or wires of the cable TV,telephone or internet provider.

OFDM has been designed to deal with these phenomena and at the same timeutilize spectrum more efficiently than spread spectrum to significantlyincrease performance. Ratified in 1999, the IEEE 802.11a standardsignificantly increases the performance (54 Mbits/s vs. 11 Mbits/s) ofindoor wireless networks.

The ability of OFDM to deal with multipath and fading is due to thenature of OFDM modulation. OFDM modulation is essentially thesimultaneous transmission of a large number of narrow band carriers,sometimes called subcarriers, each modulated with a low data rate, butthe sum total yielding a very high data rate. FIG. 1A illustrates thefrequency spectrum of multiple modulated subcarriers in an OFDM system.To obtain high spectral efficiency the frequency response of thesubcarriers are overlapping and orthogonal, hence the name OFDM. Eachnarrowband subcarrier can be modulated using various modulation formatssuch as binary phase shift keying (BPSK), quaternary phase shift keying(QPSK) and quadrature amplitude modulation (QAM) (or the differentialequivalent).

Since the bandwidth rate on each subcarrier is low, each subcarrierexperiences flat fading in multipath environment and is easy toequalize, where coherent modulation is used. The spectrums of themodulated subcarriers are not separated but overlap. The reason why theinformation transmitted over the carriers can still be separated is theso called orthogonality relation giving the method its name. Theorthogonality relation of the subcarriers requires the subcarriers to bespaced in such a way that at the frequency where the received signal isevaluated all other signals are zero. In order for this orthogonality tobe preserved it helps for the following to be true:

-   -   1. Synchronization of the receiver and transmitter. This means        they should assume the same modulation frequency and the same        time-base for transmission (which usually is not the case).    -   2. The analog components, part of transmitter and receiver, are        of high quality.    -   3. The multipath channel needs to accounted for by placing guard        intervals which do not carry information between data symbols.        This means that some parts of the signal cannot be used to        transmit information.

If the receiver and transmitter are not synchronized in frequency theorthogonality of the subcarriers is compromised and data imposed on asubcarrier may be not be recovered accurately due to inter-carrierinterference. FIG. 1B illustrates the effect of the lack ofsynchronization on the frequency spectrum of multiple subcarriers, Thedashed lines show where the spectrum for the subcarrier should be, andthe solid lines shows where the spectrum falls due to the lack ofsynchronization. Since the receiver and transmitter need to besynchronized for reliable OFDM communication to occur, but in fact inpractice they are not, it is necessary to compensate for the frequencyoffset between the receiver and the transmitter. The offset can occurdue to the inherent inaccuracy of the synthesizers and crystals in thetransmitter and receiver and to drift due to temperature or otherreasons. The offset can be compensated for at the receiver, but presentmethods only produce a coarse estimate of the actual offset. Accordingto one method for compensating for the offset, the analog signalreceived by a receiver is divided into three sections: short timingsymbol section, long timing symbol section and data symbol section. Someof the short timing symbols in the short symbol section are used forautomatic gain control and for detecting symbol timing. Other shorttiming symbols are sampled and digitized and auto-correlated to producea coarse estimate of the offset. The coarse estimate of the offset isthen used to produce a digital periodic signal whose frequency is basedon the coarse estimate of the offset. The digital periodic signal ismultiplied with digital samples of the long symbols and the product isfast fourier transformed to produce a channel estimate. The digitalcarrier is also used to multiply digital samples of the data symbols(digital data samples) when they arrive, thereby correcting for theoffset. The product of the digital carrier and the digital data samplescan now be decoded.

Since the short symbols, from which the frequency offset was derived,are relatively short, the estimate of the offset may be off appreciablyfrom the actual offset. Consequently, there will be a residual offsetwhich may cause the spectrum of one subcarrier to overlap with thespectrum of another subcarrier. Due to the overlap, when the digitaldata samples are recovered the data for one subcarrier may includeinterference from an adjacent subcarrier, degrading the throughput ofthe communication system. Furthermore, since there is a residual offset,the channel estimate is not an accurate representation of the actualtransfer function due to the channel.

As described above, existing solutions are not capable of providing arelatively good estimate of the frequency offset between a receiver andtransmitter or channel estimate. Consequently, it is desirable toprovide a solution that overcomes the shortcomings of existingsolutions.

SUMMARY

A method for correcting influence of frequency offset between a receiverand a transmitter by evaluating training symbols received during apreamble period is described. The method includes producing, based on atleast one long training symbol, a first vector whose first vector angleis indicative of a fine offset between the receiver and the transmitter,producing a fine offset estimate based on the first vector angle, andmultiplying, with a signal having a frequency based upon the fine offsetestimate, data symbols that are received after the at least one longtraining symbol is received.

BRIEF DESCRIPTION OF THE DRAWINGS

The present invention is illustrated by way of example, and notlimitation, in the figures of the accompanying drawings in which likereferences denote similar elements, and in which:

FIG. 1A illustrates the frequency spectrum of multiple modulatedsubcarriers in an OFDM system;

FIG. 1B illustrates the effect of the lack of synchronization on thefrequency spectrum of multiple subcarriers;

FIG. 2 illustrates a communication system according to one embodiment ofthe present invention;

FIG. 3 illustrates the packet structure that the IEEE 802.11a standardrequires for information transmission between two transceivers;

FIG. 4A illustrates a section of a receiver including a fine offsetadjustment circuit according to one embodiment of the present invention;

FIG. 4B illustrates a section of a receiver including a channel estimateadjustment circuit according to one embodiment of the present invention;

FIG. 4C illustrates a receiver in accordance with an embodiment of thepresent invention;

FIG. 5 illustrates a receiver in accordance with an alternativeembodiment according to the present invention;

FIG. 6 illustrates a circuit for updating the frequency offset accordingto an alternative embodiment of the present invention;

FIG. 7 illustrates a circuit for updating the frequency offset accordingto yet another alternative embodiment of the present invention;

FIG. 8 illustrates a receiver according to yet another alternativeembodiment in accordance with the present invention;

FIG. 9 shows the spectrum of received 802.11a OFDM symbols, includingcarrier leak, and a receiver's DC offset;

FIG. 10 illustrates a receiver according to yet another alternativeembodiment in accordance with the present invention;

FIG. 11A illustrates a receiver according to yet another alternativeembodiment in accordance with the present invention;

FIG. 11B illustrates numbers represented in block floating point format;

FIG. 12 illustrates a process by which a frequency domain representationis adjusted to minimize loss of information due to subsequent operationson the representation; and

FIG. 13 illustrates a receiver according to yet another alternativeembodiment in accordance with the present invention.

DETAILED DESCRIPTION

A methods and apparatus for methods and apparatus for estimating andcalculating frequency offset and for more accurately determining channelestimate are described. In the following description, for purposes ofexplanation, numerous specific details are set forth in order to providea thorough understanding of the present invention. It will be evident,however, to one skilled in the art that the present invention may bepracticed in a variety of communications signal processing circuits,especially an orthogonal frequency division multiplexing system, withoutthese specific details. In other instances, well-known operations,steps, functions and elements are not shown in order to avoid obscuringthe invention.

Parts of the description will be presented using terminology commonlyemployed by those skilled in the art to convey the substance of theirwork to others skilled in the art, such as orthogonal frequency divisionmultiplexing, fast fourier transform (FFT), inverse FFT (IFFT),autocorrelation, subcarrier, delay, and so forth. Various operationswill be described as multiple discrete steps performed in turn in amanner that is most helpful in understanding the present invention.However, the order of description should not be construed as to implythat these operations are necessarily performed in the order that theyare presented, or even order dependent. Lastly, repeated usage of thephrases “in one embodiment,” “an alternative embodiment,” or an“alternate embodiment” does not necessarily refer to the sameembodiment, although it may.

FIG. 2 illustrates a communication system according to one embodiment ofthe present invention. System 200 includes a gateway 210 that isconnected via a cable (or multiple cables) to the public switchedtelephone network (PSTN), a cable television system, an Internet serviceprovider (ISP), or some other system. Gateway 210 includes a transceiver210′ and antenna 211. Each appliance 220 includes a transceiver 220′ andantenna 221 (only one labeled). Appliance 220 could be a television,computer, telephone, or some other appliance. Transceiver 210′ providestransceiver 220′ with a wireless connection to the systems that areconnected to gateway 210. According to one embodiment, transceivers 210′and 220′ communicate in accordance with the IEEE 802.11a standard.Consequently, each of transceivers 210′ and 220′ includes a receiver anda transmitter that communicate information formatted according to the802.11a standard. In alternative embodiments, as indicated below,transceivers 210′ and 220′ may have some design features that deviatefrom the IEEE 802.11a standard.

FIG. 3 illustrates the packet structure that the IEEE 802.11a standardrequires for information transmission between two transceivers. Areceiver in transceiver 210′ or 220′ is designed to accept a packet suchas packet 300 and to derive timing information, data, and otherinformation from the packet. For example, in packet 300, the first 10symbols (t1 to t10), which are referred to as the shorts, are repeatedsequences that a receiver uses for detecting symbol timing and coarsecarrier frequency offset. GIl is the cyclic prefix of the two longsymbols T1 and T2, and is sometimes referred to as a guard intervalbecause of its use as a rough inter-symbol boundary for absorbing theeffect of multipath. GIl is made long enough such that if short symbolt10 undergoes multipath, symbol t10 will partially “smear” into GIlwithout affecting T1. T1 and T2, referred to as the longs, are used forchannel estimation, and fine symbol timing adjustment. Since OFDM isextremely sensitive to the carrier frequency offset between thetransmitter and the receiver, the present invention provides forsuccessive estimation using T1 and T2 (fine frequency offsetestimation), to reduce any residual offset after the shorts.

According to one embodiment, each short symbol takes 0.8 μs, therebyallowing altogether 8 μs to perform automatic gain control (AGC) andcoarse symbol timing and frequency offset estimation. According to oneembodiment, GIl takes 1.6 μs, which is twice the amount of the usualcyclic prefix between data symbols. After the shorts, GIl provides arough inter-symbol boundary which allows the two longs, T1 and T2, to becaptured without multipath effects from the shorts, as the relativelylong GIl is sized to provide an ample buffer zone to absorb any error insymbol boundary. According to one embodiment, T1 and T2 each take up 3.2μs, and are used to derive two estimates of the channel characteristics,as the data bits transmitted in T1 and T2 are known at the receiver. Thetwo channel estimations are combined and manipulated to form a referencechannel estimate for the following data symbols. After the longs, thepacket enters into data symbols. Each data symbol is 3.2 μs long and ispreceded by a cyclic-prefix of 0.8 μs. The cyclic prefix is used toabsorb delay spread caused by multipath so that the OFDM symbols canremain independent from each other. The first symbol is a SIGNAL symbol,which is, according to one embodiment, transmitted in binary phase shiftkeying (BPSK) with a ½-rate code. The SIGNAL symbol needs to be detectedcorrectly, as it contains the information needed for decoding the restof the packet, hence the use of BPSK with the ½-rate code. The datasymbol can be transmitted in BPSK, quaternary phase shift keying (QPSK),16-quadrature amplitude modulation (QAM), or 64-QAM with various degreesof error correction, to provide a scaleable set of data rates inresponse to different channel conditions.

FIG. 4A illustrates a section of a receiver including a fine offsetadjustment circuit according to one embodiment of the present invention.Fine offset adjustment circuit 400 includes a fine offset estimategenerator 401 that receives the long training symbols and generates afine offset estimate. Fine offset estimate generator 401, according toone embodiment, is described in greater detail below. Signal generator402 generates a digital signal having a frequency equal to the fineoffset estimate. Mixer 403 multiplies the digital signal with the datasymbols received at receiver 400 to compensate for the offset betweenreceiver 400 and a transmitter.

FIG. 4B illustrates a section of a receiver including a channel estimateadjustment circuit according to one embodiment of the present invention.Channel adjustment circuit 400 includes a channel frequency domainrepresentation generator 404 that receives the long training symbols andgenerates a channel transfer function in the frequency domain. Generator405 receives the fine offset estimate and produces a frequency domainrepresentation of a signal having a frequency equal to the fine offsetestimate. Convolver 436 convolves 1) the frequency domain representationof the signal with a frequency equal to the fine offset estimate with 2)the frequency domain representation of the channel transfer function.The output of convolver 436 is then stored in memory 441.

In contrast to memory 441, which stores an offset adjusted frequenc₁domain representation of the long symbols as received at receiver 400,memory 442 stores within it a frequency domain representation of thelong symbols as they would have been produced at a transmitter fortransmission to receiver 400. Division circuit 446 retrieves the offsetadjusted frequency domain representation of the long symbols from memory441 and divides it by memory 442's frequency domain representation ofthe long symbols as they would have been produced at a transmitter toproduce a channel estimate for storage in memory 449. While in the abovedescription₁nemory 442 stores within it a frequency domainrepresentation of the long symbols as they would have been produced at atransmitter, it should be appreciated that in an alternative embodimentmemory 442 could store a time domain representation of the long symbolsas they would have been produced at a transmitter. In such analternative embodiment, a fourier transform unit would reside in betweenmemory 442 and divider circuit 446 and would transform the time domainrepresentation in memory 442 into a frequency domain representationsuitable for being a divisor in divider circuit 447.

The channel estimate in memory 448 can be retrieved by other circuitry(not shown) and inverted and used to correct the frequency domainrepresentation of data symbols that arrive after the long symbols.

FIG. 4C illustrates a receiver 450 in accordance with an embodiment ofthe present 30 invention. Receiver 450 includes an automatic gaincontrol (AGC) circuit 413, antenna 4 i 2, an analog mixer 414, asynthesizer 416, and an analog-to-digital converter (ADC) 418. Antenna412 receives a packet (such as packet 300 described above) in the formof an analog signal transmitted by a transceiver such as transceiver210′ or 220′ described above. Since the analog signal is likely to havea varying amplitude, AGC 413 produces at its output a fixed amplitudereplica of the analog signal. According to an alternative embodiment,automatic gain control is distributed throughout the gain stages of theRF front end. It should also be appreciated that AGC 413 can be part ofa low noise amplifier (LNA) that provides gain control. Depending on thefrequency with which transceiver 210′ and 220′ are communicating,synthesizer 416 produces a synthesizer signal with a frequency such thatwhen the AGC output is multiplied with the synthesizer signal by mixer 4i 4, the analog signal is brought down to either baseband or someintermediate frequency (IF). Typically, approximately the first 6 shortsreceived are used to settle the AGC and are not used to produce a coarseoffset estimate of the offset between the synthesizers in thetransmitter and the receiver. Depending on the design of thecommunication system, a certain number of the 10 shorts are not neededto settle AGC 413. The shorts that are not needed for automatic gaincontrol can be used for coarse frequency offset estimation. When theanalog signal received includes shorts that are not needed for automaticgain control, mixer 414 produces at its output a replica of the shortsbut at baseband or the IF.

ADC 418 samples and digitizes the baseband or IF shorts to producedigital samples of the shorts. According to one embodiment, ADC 418takes 16 samples of each short symbol, which translates into a rate of20 million samples/second. In an alternative embodiment, ADC 418 takes32 samples of each short symbol, which translates into a rate of 40million samples/second. Digital mixer 420 multiplies the digital samplesof the shorts with the output of digital signal generator 422. Sincethere can be no indication of the offset until a packet is received andanalyzed, signal generator 422 initially has as an output a unit vectorwhich has zero frequency.

The output of mixer 420 is also passed to first-in-first-out (FIFO)queue 426. Queue 426 delays the digital samples of the shorts byapproximately half of the duration of the shorts that are left afterautomatic gain control has settled. For example, if 2 shorts are leftafter automatic gain control has settled, then digital samples of thefirst short are delayed by the duration of one short. If there are threeshorts, then the digital samples of the first short and half of thesamples of the second short could be delayed by the duration of one anda half shorts. Alternatively, the samples of the first two shorts of thethree shorts could be delayed by the duration of one short and the firstand second shorts could be correlated with the second and third shorts.If 4 shorts are left after automatic gain control has settled, then thedigital samples of the first two shorts are delayed by the duration oftwo shorts. Where 2 shorts are left after automatic gain control hassettled, the digital samples of the second short are changed to theircomplex conjugates by complex conjugator 428. As the complex conjugateof each sample of the second short is produced it is multiplied by itscorresponding sample from the first short in queue 426 by digital mixer430. The product of mixer 430 is then summed by integrator 432.Integrator 432's period of integration is equivalent to half the sum ofthe duration of all the shorts that are left after automatic gaincontrol has settled. So where two (four) shorts are left after automaticgain control has settled, the period of integration is the duration ofone (two) short. After all the products produced by mixer 430 have beensunned by integrator 432, the output of integrator 432 is a complexvalue or vector with an angle which is an estimate indicative of thecoarse frequency offset between the synthesizer 416 of transceiver 220′and the synthesizer (not shown) in transceiver 210′. The combination ofqueue 426, conjugator 428, and mixer 430 acts as a self-correlator orautocorrelator.

Frequency offset estimate generator 440 divides the angle of the vectoroutputted by integrator 432 by the duration of a short symbol, or moregenerally the delay of queue 426. Generator 440 produces the differencein frequency between the synthesizer 416 of transceiver 220′ and thesynthesizer (not shown) in transceiver 210′. This frequency differencebetween the synthesizers that is generated based upon the correlation ofshort symbols is referred to as a coarse frequency offset estimate. Thefrequency difference is passed to signal generator 422 which produces asinusoid with a frequency equivalent to the frequency differenceoutputted by generator 440. By having generator 422 produce a sinusoidthat has a frequency equal to the offset between the synthesizers, themismatch between the synthesizers can be compensated for.

After the shorts are correlated and a coarse offset estimate isproduced, the long symbols pass through antenna 412 and AGC 413 andarrive at mixer 414 where they are brought down to baseband or anintermediate frequency. According to one embodiment, ADC 418 samples anddigitizes the long symbols at the rate of 20 million samples a second toproduce 64 samples per long symbol. In an alternative embodiment, ADC 4i 8 produces 128 samples per long symbol, which translates into a rateof 40 million samples/second. Mixer 420 multiplies the digital longsamples with a digital sinusoid (digital periodic signal) produced bygenerator 422. Since the sinusoid produced by generator 422 is based ona coarse frequency offset estimate, at the output of mixer 420, thesamples that have been adjusted may still have a residual offset.

According to one embodiment, the output of mixer 420 that is due to thefirst long symbol is passed to a fast fourier transform (FFT) unit whichperforms a fast fourier transform of the output and stores it in memory425. Similarly, the output of mixer 420 that is due to the second longsymbol is fast fourier transformed and stored in memory 425. Averagecircuit 427 retrieves the transform of each long symbol and averagesthem and provides the average of the transforms to convolver 436.According to one embodiment the output of mixer 420 that was due to eachlong symbol was separately fourier transformed. Additionally, while theoutput of mixer 420 is fast fourier transformed according to oneembodiment, it should be appreciated that other types of transforms(e.g., hilbert transform) known in the art may be used to take a timedomain representation of a signal and transform it into a frequencydomain representation. Units that perform thetime-domain-to-frequency-domain transformation are referred to herein asfrequency domain transfer units.

The output of average circuit 427 is a frequency domain representationof the two long symbols as they have been modified by the channelbetween the two transceivers. As described below, this frequency domainrepresentation of the two long symbols can be used to generate anestimate of the transfer function of the channel (or channel estimate).The channel estimate can be inverted and used to reverse the effect ofthe channel on the signal transmitted by transceiver 210′. Since thesamples which were fast fourier transformed were multiplied by asinusoid with a frequency based on the coarse offset estimate, thefrequency domain representation of the received signal may contain aresidual offset. Consequently, the frequency domain representationproduced by average circuit 427 cannot be used to produce an accuraterepresentation of the actual channel transfer function until anyresidual offset is compensated for. Any residual offset can becompensated for after a fine offset estimate is generated using thesamples of the long symbols.

To produce a fine offset estimate, the samples of the long symbolsproduced at the output of ADC 418 must first pass through queue 426 andconjugator 428. Queue 426 delays the digital samples of the first longsymbol of the two long symbols by the duration of one long symbol. Thedigital samples of the second long are changed to their complexconjugates by complex conjugator 428. As the complex conjugate of eachsample of the second long is produced it is multiplied by itscorresponding sample from queue 426 by digital multiplier 430. Theproducts of multiplier 430 are summed by integrator 432. After all theproducts produced by multiplier 430 have been summed by integrator 432,the output of integrator 432 is a complex value or vector with an anglewhich is an estimate indicative of the fine frequency offset between thesynthesizers of transceivers 210′ and 220′.

Frequency offset estimate generator 440 divides the angle of the vectoroutputted by integrator 432 by the duration of a long symbol, or moregenerally the time between the starts of the two longs. Generator 440produces the residual difference in frequency between the synthesizersin transceiver 210′ and transceiver 220′. Since digital long sampleswere already multiplied by a signal with a frequency based on the coarseoffset estimate, the output of generator 440 is the residual frequencydifference between the synthesizers in transceivers 210′ and 220′. Thisfrequency difference between the synthesizers that is generated basedupon the correlation of long symbols is referred to as a fine offsetestimate. The fine offset estimate is passed to signal generator 422which produces a sine wave with a frequency equivalent to the sum of thefine frequency offset estimate and the coarse frequency offset estimate.By having generator 422 produce a sinusoid that has a frequency equal tothe residual offset between the synthesizers, the mismatch between thesynthesizers can be further compensated for.

As indicated above, since the digital long samples which were fastfourier transformed by FFT unit 424 were multiplied by a signal with afrequency equal to the coarse offset estimate, the frequency domainrepresentation of the received signal may not be a very accuraterepresentation of the actual transmitted signal as transformed by thechannel. The inaccuracy is partly due to the presence of a residualfrequency offset. The residual frequency offset can be estimated andcompensated for using the fine offset estimate. Since the frequencydomain representation of the received signal is stored in memory 425,the frequency domain representation of the received signal needs to beconvolved by a frequency domain representation of a signal that has afrequency equal to the fine offset estimate, fo. The frequency domainrepresentation of a windowed complex sine wave that is sampled for afinite period of time has the general shape of a sinc function—sin(x)/x.The frequency domain representation of the windowed sine wave varies asa function of fo. According to one embodiment, convolver 436 convolvesthree samples of the frequency domain representation of a sine wave,with frequency equal to the fine offset estimate, with the frequencydomain representation of the received signal stored in memory 425. Thethree samples of the frequency domain representation of the sine wavewith frequency equal to the fo are retrieved from memory 438 byfrequency domain compensator 434. In order to perform the convolution asrapidly as possible, memory 438 stores a table that has for variousvalues of fo associated samples of the frequency domain representationof a sine wave with frequency equal to fo. To retrieve the appropriatesamples, compensator 434 first calculates the fine offset estimate, fo,based on the output of integrator 432 and then indexes into the tablebased on fo. In one embodiment, compensator 434 retrieves only theclosest entry to fo. In another embodiment, if the calculated fineoffset estimate falls between two values of fo in memory 438,compensator 434 retrieves the samples that are associated with the twovalues. Compensator 434 then interpolates between each sample of onevalue and the corresponding sample of the other value to produce aninterpolated sample value. Compensator 434 then provides theinterpolated sample values for the calculated fine offset estimate toconvolver 436 which then convolves the interpolated sample values withthe frequency domain representation of the long symbols as modified bythe channel. The output of convolver 436 is a frequency domainrepresentation of the long symbols as received at the receiver and asadjusted for frequency offset between the transmitter and receiver. Theoutput of convolver 436 is then stored in memory 441.

In contrast to memory 441, which stores an offset adjusted frequencydomain representation of the long symbols as received at receiver 450,memory 442 stores within it a frequency domain representation of thelong symbols as they would have been produced at transceiver 210′ fortransmission to receiver 450. Circuit 446 retrieves the offset adjustedfrequency domain representation of the long symbols from memory 441 anddivides it by memory 442's frequency domain representation of the longsymbols as they would have been produced at transceiver 210′ to producea channel estimate for storage in memory 448. While in the abovedescription memory 442 stores within it a frequency domainrepresentation of the long symbols as they would have been produced attransceiver 210′, it should be appreciated that in an alternativeembodiment memory 442 could store a time domain representation of thelong symbols as they would have been produced at transceiver 210′. Insuch an alternative embodiment, a fourier transform unit would reside inbetween memory 442 and circuit 446 and would transform the time domainrepresentation in memory 442 into a frequency domain representationsuitable for being a divisor in circuit 446.

The channel estimate in memory 448 can be retrieved by other circuitry(not shown) and inverted and used to correct the frequency domainrepresentation of data symbols that arrive after the long symbols.

While in the above description offset compensator 434 retrieves frommemory 438 three samples of the frequency domain representation of asinusoid with frequency equivalent to the fine offset estimate, in analternative embodiment, compensator 434 stores an equation for each ofthe samples. The equation describes how the complex values of the samplevaries as a function of the fine offset estimate. After compensator 434calculates the fine offset estimate, compensator 434 evaluates eachsample's equation to determine each sample's value for the calculatedfine offset estimate. Compensator 434 then supplies the sample values toconvolver 436 which convolves them with frequency domain representationof the received signal stored in memory 425.

While in the above description lookup table 438 stores only three samplevalues for each fine offset estimate value, it should be appreciatedthat the actual number of sample values stored for each fine offsetestimate value can be a number other than three and is dependent ondesign considerations. Similarly, while in the above description threeequations are stored in compensator 434, it should be appreciated thatthe actual number of equations is a design consideration and may not bethree, but equal to the number of samples that are needed.

FIG. 5 illustrates a receiver 500 in accordance with an alternativeembodiment according to the present invention. Receiver 500 operates inthe manner that is similar to receiver 450. Consequently, it is notnecessary to repeat the description of the operation of most of theelements. The difference between receiver 500 and receiver 450 lies inthe manner in which a channel estimate is performed. Rather than fouriertransforming the output of mixer 420, the output of mixer 420 that isdue to the long symbol samples (coarse offset adjusted long symbolsamples) is stored in memory 520 until integrator 432 has produced avector with an angle which is an estimate indicative of the fine offsetbetween the synthesizers of transceivers 210′ and 220′. When integrator432 produces an angle which is an estimate indicative of the fineoffset, signal generator 524 calculates the fine offset estimate bydividing the angle by the duration of a long symbol, or more generallythe duration of the integration by integrator 432. Signal generator 524then generates a digital sinusoid with a frequency equal to the fineoffset estimate. Mixer 522 retrieves from memory 520 the coarse offsetadjusted long symbol samples of the first long symbol and multipliesthem with a digital sinusoid produced by generator 524. The output ofmixer 522 is then fourier transformed by FFT unit 526, and the output ofFFT unit 526 is stored in memory 527. Mixer 522 then retrieves frommemory 520 the coarse offset adjusted long symbol samples of the secondlong symbol and multiplies them with the digital sinusoid produced bygenerator 524. The output of mixer 522 is then fourier transformed byFFT unit 526, and the output of FFT unit 526 is stored in memory 527.Average circuitry 528 retrieves the transforms of each offset adjustedlong symbol, averages the transforms, and stores the average in memory440.

According to one embodiment, units 510 and 526 are the same unit. Oncethe coarse and fine offsets have been calculated, FFT unit 510 producesat its output fourier transformed representations of data symbols andguard intervals. The output of unit 510 is used, in embodimentsdescribed below, to provide updated estimates of the offset between thereceiver and transmitter.

The description given above in connection with FIG. 4C including thealternative embodiments also applies to FIG. 5, and need not be repeatedhere.

In the above description, the frequency offset was estimated byauto-correlating either the long or short symbols. The frequency offsetcan also be updated during receipt of the data symbols. During receiptof the data symbols, the frequency offset between the transceivers canbe estimated again by estimating the difference between the phase of thepilot carriers in a data symbol and the phase of the pilot carriersduring the long symbols. FIG. 6 illustrates a circuit 600 for updatingthe frequency offset according to an alternative embodiment of thepresent invention. In circuit 600, the divider circuit 610 receives theoutput of FFT unit 605 and the output of memory 448 that stores thechannel estimate. FFT unit 605 produces a frequency domainrepresentation of a received data symbol. Divider circuit 610 dividesthe output of FFT unit 605 by the channel estimate.

According to one embodiment, the output of unit 605 is 64 samples of thefrequency domain representation of the received data symbol. In analternative embodiment, the output of unit 605 is 128 samples of thefrequency domain representation of the received signal. It should beappreciated that the number of samples is a design consideration and canbe tied to the number of samples produced for each long timing symbol byADC 418. In the embodiment where unit 605 produces 64 samples, thesamples represent a frequency band extending from −10 MHz to +10 MHz.Since only 16.5 MHz is used for transmitting data, there are 52 samplesthat represent data transmission and the remaining samples simplyrepresent a guard band between the 20 MHz wide channels of an 802.11astandard compliant system. In the case of 128 samples, the outer 64 areadjacent channels. The 52 samples represent 52 carriers of which fourare pilot carriers which are used to monitor signal strength and carrierphase. According to one embodiment, the ±7 and ±21 samples are samplesof pilot carriers. When circuit 610 divides the 64 samples of thefrequency domain representation of the received data symbol by thechannel estimate, the phase of the quotient for the samples at which apilot carrier is present is indicative of the difference between thephase in a pilot carrier of the data symbol and the phase in thecorresponding pilot carrier in the long symbols. Average offset circuit620 selects the quotients for the samples at which a pilot carrier ispresent and determines the average phase difference by adding up thephase difference for each of the pilot carriers and dividing the sum bythe number of pilot carriers, which is four according to one embodiment.

According to one embodiment, if the magnitude of the smallest pilotcarrier is less than one eighth of the magnitude of the largest pilotcarrier, the quotient phase of the smallest pilot carrier is notincluded in determining the average phase difference. Rather, circuit620 throws out the angle of the smallest carrier and derives areplacement angle using linear interpolation and the angles of thequotients of the two nearest pilot carrier neighbors. The average phasedifference is then derived by adding up the phase difference for each ofthe pilot carriers, including the replacement angle for the smallestquotient, and dividing the sum by the number of pilot carriers, which isfour according to one embodiment.

After determining the average phase difference, circuit 620 divides thedifference by the time elapsed since the fine offset estimate wascalculated to determine an updated frequency offset which is a measureof the frequency offset that remains between the transceivers even aftercorrection using the coarse and fine offset estimates. The updatedfrequency offset is then applied to digital signal generator produces adigital sinusoid to correct for the frequency mismatch between thetransmitter and receiver. The frequency of the sinusoid is the sum ofthe updated frequency offset and the coarse and fine offset estimates.

It should be appreciated that updating the frequency offset bydetermining the phase difference between the pilots in the channelestimate and the pilots in a data symbol as just described in connectionwith FIG. 6 can also be used in the embodiment described in connectionwith FIG. 5. In such an embodiment, divider circuit 610 would accept theoutput of FFT unit 510 and the channel estimate from memory 448.

The frequency offset can also be updated by measuring the difference inthe phase of a pilot channel in two data symbols or by measuring thedifference in phase between the terminal portion of a data symbol andthe data symbol's cyclic prefix (or guard interval). The phasedifference in a pilot channel in two data symbols divided by the timeelapsed between the two data symbols is a measure of the frequencyoffset between the transceivers. Similarly, the phase difference betweenthe terminal portion of a data symbol and its cyclic prefix divided bythe time elapsed between the two is a measure of the frequency offsetbetween the transceivers, FIG. 7 illustrates a circuit 700 for updatingthe frequency offset according to yet another alternative embodiment ofthe present invention. While circuit 700 will be described in terms ofcalculating the frequency offset, by estimating the phase difference ina pilot channel in two data symbols, it should be appreciated thatcircuit 700 can also be used to estimate the phase difference between aterminal portion of a data symbol and the symbol's guard interval. Incircuit 700, the divider circuit 710 receives the output of unit 705that is due to a data symbol at time T₀ and stores the output in memory712. At some time T₀+Δt, where Δt is equal to an integer multiple of theduration of a data symbol, divider circuit 710 accepts the output ofunit 705 that is due to another data symbol and stores the output inmemory 712. Unit 705 produces a frequency domain representation of thereceived signal. divider circuit 710 divides the frequency domainrepresentation of the first data symbol that is stored in memory 712 bythe frequency domain representation of the second data symbol.

According to one embodiment, the output of convolver 436 is 64 samplesof the frequency domain representation of a data symbol. In analternative embodiment, the output of unit 705 is 128 samples of thefrequency domain representation of the received signal. It should beappreciated that the number of samples is a design consideration and canbe tied to the number of samples produced by ADC 418 per long timingsymbol. In the embodiment where convolver 436 produces 64 samples, thesamples represent a frequency band extending from −10 MHz to +10 MHz.Since only 16.5 MHz of the 20 MHz is used for transmitting data, thereare 52 samples that represent data transmission and the remainingsamples simply represent a guard band between the 20 MHz wide channelsof an 802.11a standard compliant system. The 52 samples represent 52carriers of which four are pilot carriers which are used to monitorsignal strength. According to one embodiment, the ±7 and ±21 samples aresamples of pilot carriers. When circuit 710 divides the 64 samples ofthe frequency domain representation of the first data symbol stored inmemory 712 by frequency domain representation of the second data symbol,the phase of the quotient for the samples at which a pilot carrier ispresent is indicative of the difference between the phase in a pilotcarrier of the first data symbol and the phase in the correspondingpilot carrier in the second data symbol. Average offset circuit 720selects the quotients for the samples at which a pilot carrier ispresent and determines the average phase difference by adding up thephase difference for each of the pilot carriers and dividing the sum bythe number of pilot carriers, which is four according to one embodiment.

According to one embodiment, if the magnitude of the smallest quotientof a pilot carrier is less than one eighth of the magnitude of thelargest pilot carrier, the phase of the smallest quotient of a pilotcarrier is not included in determining the average phase difference.Rather, circuit 720 throws out the angle of the smallest pilot andderives a replacement angle using linear interpolation and the angles ofthe quotients of the two nearest pilot carrier neighbors. The averagephase difference is then derived by adding up the phase difference foreach of the pilot carriers, including the replacement angle for thesmallest quotient, and dividing the sum by the number of pilot carriers,which is four according to one embodiment.

After determining the average phase difference, circuit 720 divides thedifference by the time elapsed between the receipt of the two datasymbols at the antenna 412 to determine the measure of the frequencyoffset between the transceivers. This updated frequency offset is thenapplied to digital signal generator 422 which adds the updated frequencyoffset to the coarse and fine offsets and produces a digital sinusoid tocorrect for the frequency mismatch between the transmitter and receiver.

It should be appreciated that updating the frequency offset bydetermining the phase difference between the pilots in two differentdata symbols as just described in connection with FIG. 7 can also beused in the embodiment described in connection with FIG. 5. In such anembodiment, divider circuit 710 would accept the output of FFT unit 510.

FIG. 8 illustrates a receiver 800 according to yet another alternativeembodiment in accordance with the present invention. Receiver 800operates in the manner that is similar to receiver 450. Consequently itis not necessary to repeat the description of the operation of most ofthe elements. The difference between receiver 800 and receiver 450 liesin the enhancement in receiver 800 which allows the coarse and finefrequency offsets to be determined more accurately. Receiver 800'senhancement is a filter 810 for removing the DC offset in the samplesthat emerge from mixer 420. According to one embodiment, filter 810 is alow-pass infinite impulse response (IIR) filter, but alternativeembodiments may have a different type of filter. Integrator 820 sums thelow-pass filtered samples that emerge from filter 810 with the samplesthat emerge from mixer 420. Since the DC component of the samples isremoved, the angles that emerge from integrator 432 are more accurate.Consequently, the fine and coarse offset estimates are more accurate.

An alternative way to compensate for the DC present in the signal is tocalculate the DC offset present in the shorts and the longs. Since thereis a carrier frequency offset between the transmitter and the receiver,the DC offset introduced by the receive chain is not at the DC of thetransmitted OFDM signal spectrum. If this carrier frequency offset iscorrected before the DC offset correction, then the receiver DC offsetwill be moved to the frequency with an opposite sign of the carrierfrequency offset. For example, an uncertainty of 40 parts per million(ppm) in a carrier whose frequency is 5.25 GHz corresponds to an offsetof 210 KHz, about ⅔ of the frequency separation between carriers.

FIG. 9 shows the spectrum of received 802.11a OFDM symbols, includingcarrier leak, and a receiver's DC offset. As shown in FIG. 9, for anynon-zero frequency offset, the receiver DC offset would containcontributions from nearby data bins. The DC offset estimation would havebeen easier if the transmitted signal spectrum indeed had a zero DC, asimplied in the 802.11a standard's OFDM modulation. However, there isalways a certain amount of carrier leak from the power amplifier at thecarrier frequency, which translates to the DC bin after down conversion,and therefore the DC in the transmitted signal spectrum is not exactlyzero. According to the 802.11a standard, the power of the carrier leakcan be as high as 15 dB below the signal power. Assuming each of thedata carriers has about the same amount of power, the power of thecarrier leak can actually be higher than the power of each data carrier(−15 dB>1/52), and therefore cannot be ignored.

According to one implementation, the receiver DC offset can be as largeas +/−100 mV. Since, according to one embodiment, the full range of ADC418 is from −500 mV to 500 mV, the power of the DC offset can besignificantly higher than the power of one data carrier.

Most DC offset algorithms use filters. However, since there aretypically only 4×32=128 samples left in the shorts, the bandwidth of thefilter cannot be very narrow. As shown in FIG. 9, any filteringoperation with a bandwidth larger than the carrier frequency offsetwould pass both the carrier leak and the DC offset, and therefore cannotbe an accurate DC offset estimator. To separate the DC offset from therest of the signal spectrum, we have to rely on the fact that thecarrier leak is in frequency lock with the data carriers, while the DCoffset is plainly a signal added in at the receiver.

FIG. 10 illustrates a receiver 1000 according to yet another alternativeembodiment in accordance with the present invention. Receiver 1000operates in the manner that is similar to receiver 450. Consequently itis not necessary to repeat the description of the operation of most ofthe elements. The difference between receiver 1000 and receiver 450 liesin the enhancement in receiver 1000 that allows the fine frequencyoffset to be determined more accurately. Receiver 1000's enhancement isadditional circuitry for determining the DC offset. Receiver 1000separates the receiver DC offset from the transmitted spectrum, bytaking two snapshots of the same transmitted symbol and calculating theDC offset from the difference of these two snapshots. Since the shortsare a repetitive sequence of the same symbol, two shorts are used tocalculate the DC offset. If AGC 413 completes its operation quicklywithout taking up too many short symbols, the remaining short symbolscan be used for a more accurate estimation. According to one embodiment,2 short symbols are used for coarse DC offset calculation based on thecoarse symbol timing. It should be appreciated that the number of shortsymbols used for DC offset calculation is design dependent and that theinvention encompasses using a number of short symbols other than 2.

If the coarse frequency offset is known, the phase difference, α,between 32 samples (or 64 samples if 4 short symbols are available) canbe calculated. The sign of α is defined such that if the transmittercarrier frequency is higher than receiver carrier frequency, α ispositive. This factor will be used to correct the DC offset calculationat the end of the short symbols. If there is a non-zero frequencyoffset, the transmitted signal spectrum will rotate, as compared to theDC offset introduced at the receiver, by this amount of phase for every32 samples. If the two short symbols are accumulated separately andreferred to as x1 and x2, then the DC offset can be calculated asfollows:

$\begin{matrix}{{D\; C\mspace{14mu}{offset}} = \frac{\left( {{x1} - {x2}} \right){\mathbb{e}}^{({j\;\alpha})}}{32\left( {1 - {\mathbb{e}}^{({j\;\alpha})}} \right)}} & \left( {{Equation}\mspace{14mu} 2} \right)\end{matrix}$

Receiver 1000 includes an integrator 1010 that subtracts out the DCoffset from symbols that 5 are received after the short symbols used forDC offset measurement are received. Since the DC offset cannot bemeasured until the short symbols have been received and used todetermine the coarse frequency offset, according to one embodiment,integrator 1010 allows the samples of the short symbols to passunaffected. In the event only two shorts can be used for DC offsetcalculation, integrator 1020 accumulates the samples of the first shortsymbol (or the first two short symbols where four shorts are used for DCoffset calculation) and provides the sum to DC offset compensator 1030.Integrator 1020 then accumulates the samples of the second short symbol(or the last two short symbols where four shorts are used for DC offsetcalculation) and provides the sum to compensator 1030. When integrator432 has produced the coarse offset estimate as described above inconnection with FIG. 4C, compensator 1030 evaluates equation 2 above todetermine the DC offset. The DC offset evaluated using equation 2 ismore accurate when the frequency offset is large, so that (1−e^(jα))will not be a very small number in the denominator, than when thefrequency offset is small. If the frequency offset is actually verysmall, in which case (1−e^(jα)) will be very close to zero, the aboveequation would incur too much of noise enhancement to be useful. If thefrequency offset is indeed very small, the filtering technique describedin connection with FIG. 8 would work just fine as the carrier leakshould be considered as part of the DC offset (they overlap in thefrequency spectrum).

Since the coarse offset is available at the end of the shorts,compensator 1030 either uses the above equation and the coarse offset todetermine the DC offset, when the frequency offset is relatively large,or compensator 1030 simply uses (x1+x2)/64 (Equation 3) to calculate theDC offset, when the frequency offset is small.

A fine DC offset estimate can be calculated when more than two shortsymbols are available for DC offset estimation. In an alternativeembodiment, samples from four short symbols are used for fine DC offsetestimation.

FIG. 11A illustrates a receiver 1100 according to yet another embodimentof the present invention. Receiver 1100 operates in a manner similar toreceiver 450. Consequently, the operation of most of the elements neednot be repeated here. Receiver 1100 is able to produce relatively moreaccurate channel estimates because it has a gain up circuit 1110 thatchanges the output of FFT unit 424 50 that loss of information in theoutput due to later operations such as smoothing and inversion isminimized. According to one embodiment, unit 424 produces values in ablock floating point format. The block floating point format providessome of the benefits of floating point format, but with less overhead byscaling blocks of numbers rather than each individual number. FIG. 11Billustrates numbers represented in block floating point format. In blockfloating point format, a block of numbers (i.e., several mantissas)share one exponent. Assuming the output of unit 424 is due to receipt ofthe first long symbol at the receiver, unit 424 puts out numbers whichare the frequency domain representation of the long symbol and which areformatted in accordance with the block floating point format. The numberof bits in the mantissa and exponents is a design consideration, and thepresent invention encompasses many different combinations. For purposesof illustration only, according to one embodiment, the mantissa is 16bits long and the exponent is 4 bits long. According to one embodiment,adders and multipliers which perform operations on the 16-bit numbersuse 17 bit registers for the mantissas and 5 bit registers for theexponents. Since, in performing computations, it is desirable forpurposes of minimizing loss of information to use as much of the wordlength of the registers as possible without causing an overflow, if thenumbers produced by unit 424 are relatively small it is beneficial tohave them scaled so that they use as much of the word length aspossible. The amount of scaling is dependent upon how much ‘headroom’ isneeded in order to avoid overflow. For example, if mantissas are 16-bitslong, numbers are scaled up to the 14th bit, with two bits left forheadroom.

FIG. 12 illustrates a process 1200 for scaling a frequency domainrepresentation of a signal to minimize loss of information. According toone embodiment, gain up circuit 1110 performs a process such as process1200. Gain up circuit 1110 sets (1205) variable MaxCoeff to 0. Circuit1110 then retrieves (1210) from memory (not shown) the first real andimaginary coefficients that it received from unit 424, and examines(1215) the size of each of the coefficients to determine if either isgreater than MaxCoeff. If either is larger than MaxCoeff, circuit 1110assigns (1220) the larger of the two coefficients to MaxCoeff. Circuit1110 then determines (1125) whether more coefficients are to beretrieved from unit 424. If there are more coefficients to be retrievedfrom unit 424, circuit 1110 retrieves (1230) the next pair ofcoefficients and returns to determine (1215) whether either of thecoefficients is greater than MaxCoeff. If there are no morecoefficients, circuit 1110 determines (1235) whether MaxCoeff is greaterthan a threshold that has been selected so that numbers can be properlyrepresented by the registers during calculations involving the numbers.According to one embodiment, the threshold is the number which has the14th bit set, or 16,384. If MaxCoeff is less than the threshold, circuit1110 determines (1240) the minimum numbers of left shifts of MaxCoeffthat will make MaxCoeff greater than or equal to the threshold. Afterdetermining the minimum number of left shifts, circuit 1110 left shifts(1245) each coefficient received from unit 424 by the minimum number ofleft shifts and adjusts the exponent of the block to reflect that thecoefficients have been left shifted. If MaxCoeff is greater than thethreshold, circuit 1110 provides (1250) the coefficients received fromunit 424 to averaging circuit 425. Alternatively, the largest mostsignificant bit position of the coefficients can be determined, anddepending on how it compares to the threshold, the exponent of the blockmay be adjusted and the coefficients left shifted.

After averaging circuit 425 receives the transforms for the two longsymbols, it averages the transforms and provides the average toconvolver 436. As described above in connection with FIG. 4, convolver436 convolves the average of the transforms with a frequency domainrepresentation of a sinusoid in order to minimize the effect of anyresidual offset. The operation of circuit 1100 from received signalstorage 440 up to memory 448 is as described above and need not berepeated.

After the channel estimate arrives at memory 448, smoothing circuit 1120retrieves the channel estimate from memory 448 and smoothes it using afinite-impulse response (FIR) filter which has seven taps according toone embodiment, but other numbers of taps are also possible and aredesign dependent. The smoothing lessens the effect of noise on thevalues of the channel estimate. Inversion circuit 1130 then inverts thesmoothed channel estimate and stores the inverted and smoothed channelestimate until the frequency domain representation of a data symbolarrives at multiplier 1140.

Before samples of a data symbol can arrive at multiplier 1140 they firsthave to reach unit 424. The operation of the elements between antenna 4i 2 and multiplier 420, which produces a digital time domainrepresentation of a data symbol at baseband or IF, is as described abovein connection with FIG. 4 and need not be repeated here. Unit 424fourier transforms the offset corrected digital time domainrepresentation of a data symbol after it emerges from multiplier 420.Gain up circuit 1110 scales the frequency domain representation of thedata symbol in the manner that scaling is described above in connectionwith FIG. 12. Multiplier 1140 multiplies the scaled frequency domainrepresentation of the data symbol with the inverted and smoothed channelestimate from circuit 1120 to produce a frequency domain representationof the data symbol which equalizes the effect of the channel.

FIG. 13 illustrates a receiver 1300 according to yet another embodimentof the present invention. Receiver 1300 largely operates in a mannerthat is similar to receiver 1100, and the operation of most of itselements need not be repeated here. The essential differences lie in thefact that before multiplication occurs by multiplier 1340 gain up inreceiver 1300 occurs only for the channel estimate and not the datasymbols. Consequently, gain up is necessary after multiplier 1340. Gainup only occurs for the channel estimate because the frequency domainrepresentation of a data symbol leaves unit 424 and arrives atmultiplier 1340 without any intervening gain up. Gain up circuit 1310operates in the same manner as gain up circuit 1110 and need not bedescribed again here. Gain up repeater circuit 1350, on the other hand,according to one embodiment, does not perform process 1200, but in analternative embodiment it may. Repeater circuit 1350 receives from gainup circuit 13 10 the number of minimum left shifts that were performedon the coefficients of the frequency domain representations of the longsymbols. Repeater circuit 1350 performs the same number of minimum leftshifts on the output of multiplier 1340. In the embodiment whererepeater circuit 1350 repeats process 1200, circuit 1350 does notreceive from circuit 1310 the number of minimum left shifts that wereperformed on the coefficients of the frequency domain representations ofthe long symbols.

Thus, methods and apparatus for estimating and calculating frequencyoffset and for more accurately determining the channel estimate havebeen described. Although the present invention has been described withreference to specific exemplary embodiments, it will be evident to oneof ordinary skill in the art that various modifications and changes maybe made to these embodiments without departing from the broader spiritand scope of the invention as set forth in the claims. Accordingly, thespecification and drawings are to be regarded in an illustrative ratherthan a restrictive sense.

1. A method for correcting influence of frequency offset between areceiver and a transmitter by evaluating training symbols receivedduring a preamble period, the method comprising: producing, based on atleast one training symbol, a first vector whose first vector angle isindicative of a fine offset between the receiver and the transmitter;producing a fine offset estimate based on the first vector angle; andmultiplying, with a signal having a frequency based upon the fine offsetestimate, data symbols that are received after the at least one trainingsymbol is received.
 2. The method of claim 1, further comprising:producing, based on the first vector angle, a frequency domainrepresentation of a second signal having a second frequencysubstantially equivalent to the fine offset estimate; and convolving thefrequency domain representation of the second signal with a frequencydomain representation of the at least one training symbol received atthe receiver to produce an offset compensated frequency domainrepresentation of the at least one training symbol that has effect ofthe frequency offset on channel transfer function between the receiverand the transmitter substantially removed.
 3. The method of claim 2,producing, based on the at least one training symbol received at thereceiver, the frequency domain representation of the at least onetraining symbol received at the receiver.
 4. The method of claim 3,further comprising producing a channel estimate by dividing the offsetcompensated frequency domain representation of the at least one trainingsymbol received at the receiver by a frequency domain representation ofat least one training symbol that is substantially representative of theat least one training symbol as transmitted by the transmitter.
 5. Themethod of claim 3, wherein the frequency domain representation of the atleast one training symbol includes a frequency domain representation ofa first training symbol and a frequency domain representation of asecond training symbol, the method further comprising: producing anaverage of the frequency domain representation of the at least onetraining symbol by averaging the frequency domain representation of thefirst training symbol and the frequency domain representation of thesecond training symbol; producing the offset compensated frequencydomain representation of the at least one training symbol based on theaverage by convolving the average of the frequency domain representationof the at least one training symbol with a frequency domainrepresentation of a third signal; producing a channel estimate bydividing the offset compensated frequency domain representation of theaverage with a frequency domain representation of the at least onetraining symbol that is substantially representative of the at least onetraining symbol as transmitted by the transmitter.
 6. The method ofclaim 5, further comprising: producing the frequency domainrepresentation of the at least one training symbol that is substantiallyrepresentative of the at least one training symbol as transmitted by thetransmitter.
 7. The method of claim 4, further comprising: dividing anoffset compensated frequency domain representation of a data symbol bythe channel estimate to produce a representation of phase differencebetween at least one pilot in the data symbol and at least one pilot inthe at least one training symbol; and producing, based on therepresentation of phase difference, an average of the phase differencebetween the at least one pilot in the data symbol and the at least onepilot in the at least one training symbol, and, based on the average ofthe phase difference, an updated frequency offset for application to afirst signal generator.
 8. The method of claim 4, further comprising:providing an offset compensated frequency domain representation of afirst data symbol and an offset compensated frequency domainrepresentation of a second data symbol; dividing the offset compensatedfrequency domain representation of the first data symbol by the offsetcompensated frequency domain representation of the second data symbol toproduce a representation of phase difference between at least one pilotin the first data symbol and at least one pilot in the second datasymbol; and producing, based on the representation of phase difference,an average of the phase difference between the at least one pilot in thefirst data symbol and the at least one pilot in the second data symbol,and, based on the average of the phase difference, an updated frequencyoffset for application to a first signal generator.
 9. The method ofclaim 1, further comprising: producing, based on the first vector angle,a first time domain periodic signal; and multiplying a time domainrepresentation of the at least one training symbol with the first timedomain periodic signal to produce an offset compensated time domainrepresentation of the at least one training symbol.
 10. The method ofclaim 9, further comprising: transforming the offset compensated timedomain representation of the at least one training symbol to produce anoffset compensated frequency domain representation of the at least onetraining symbol received at the receiver; and producing a channelestimate by dividing the offset compensated frequency domainrepresentation of the at least one training symbol received at thereceiver by a frequency domain representation of the at least onetraining symbol that is substantially representative of the at least onetraining symbol as transmitted by the transmitter.
 11. The method ofclaim 10, further comprising: providing the frequency domainrepresentation of the at least one training symbol that is substantiallyrepresentative of the at least one training symbol as transmitted by thetransmitter.
 12. The method of claim 10, further comprising: dividing anoffset compensated frequency domain representation of a data symbol bythe channel estimate to produce a representation of phase differencebetween at least one pilot in the data symbol and at least one pilot inthe at least one training symbol received at the receiver; producing,based on the representation of phase difference, an average of the phasedifference between the at least one pilot in the data symbol and the atleast one pilot in the at least one training symbol received at thereceiver, and, based on the average of the phase difference, an updatedfrequency offset for application to a first signal generator.
 13. Themethod of claim 10, further comprising: providing an offset compensatedfrequency domain representation of a first data symbol and an offsetcompensated frequency domain representation of a second data symbol;dividing the offset compensated frequency domain representation of thefirst data symbol by the offset compensated frequency domainrepresentation of the second data symbol to produce a representation ofphase difference between at least one pilot in the first data symbol andat least one pilot in the second data symbol; and producing, based onthe representation of phase difference, an average of the phasedifference between the at least one pilot in the first data symbol andthe at least one pilot in the second data symbol, and, based on theaverage of the phase difference, an updated frequency offset.
 14. Themethod of claim 1, further comprising: receiving samples of shorttraining symbols; producing filtered samples of the short trainingsymbols based on the received samples of the short training symbols; andsubtracting the filtered samples of the short training symbols from thereceived samples of the short training symbols to produce short trainingsymbol samples that have direct current substantially removed.
 15. Themethod of claim 1, further comprising: producing a second vector, basedon summing samples of at least one short training symbol that have notbeen compensated for frequency offset, and a third vector, based onsumming samples of another at least one short training symbol that havenot been compensated for frequency offset; calculating a direct currentoffset by evaluating$\frac{\left( {{x1} - {x2}} \right){\mathbb{e}}^{({j\;\alpha})}}{N\left( {1 - {\mathbb{e}}^{({j\;\alpha})}} \right)}$wherein α is the first vector angle, x1 is the second vector, x2 is thethird vector, and N is number of samples in the at least one shorttraining symbol that have not been compensated for frequency offset; andproducing a difference between samples of symbols received after theshort training symbols and the direct current offset.
 16. The method ofclaim 1, further comprising: producing a second vector, based on summingsamples of at least one short training symbol that have not beencompensated for frequency offset, and a third vector, based on summingsamples of another at least one short training symbol that have not beencompensated for frequency offset; calculating a direct current offset byevaluating $\frac{\left( {{x1} - {x2}} \right)}{2N}$ wherein x1 is thesecond vector, x2 is the third vector, and N is number of samples in theat least one short training symbol that have not been compensated forfrequency offset; and producing a difference between samples of symbolsreceived after the short training symbols and the direct current offset.17. An automatic frequency control circuit for correcting influence offrequency offset between a receiver and a transmitter by evaluatingtraining symbols received during a preamble period, the circuitcomprising: an autocorrelator that is to produce, based on shorttraining symbols, a first vector whose first vector angle is indicativeof a coarse offset between the receiver and the transmitter and is toproduce, based on at least one long training symbol, a second vectorwhose second vector angle is indicative of a fine offset between thereceiver and the transmitter; a frequency offset generator that is toproduce a coarse offset estimate based on the first vector angle and afine offset estimate based on the second vector angle; a first signalgenerator that is to produce, based on the coarse offset estimate, afirst periodic signal with a first frequency equivalent substantially tothe coarse offset estimate; a first mixer that is to produce a productof the at least one long training symbol received at the receiver andthe first periodic signal and apply the product to the autocorrelator,wherein the autocorrelator is to produce the second vector based on theproduct; wherein, after the fine offset estimate is produced by thefrequency offset generator, the first signal generator is to produce asecond periodic signal with a second frequency based upon the coarseoffset estimate and the fine offset estimate; and wherein the firstmixer is to multiply, with the second periodic signal, symbols that arereceived after the at least one long training symbol is received. 18.The circuit of claim 17, further comprising: an offset compensator thatis to produce, based on the second vector angle, a frequency domainrepresentation of a third signal having a third frequency substantiallyequivalent to the fine offset estimate; and a convolver that is toconvolve the frequency domain representation of the third signal with afrequency domain representation of the at least one long training symbolreceived at the receiver to produce an offset compensated frequencydomain representation of the at least one long training symbol that haseffect of the frequency offset between the receiver and the transmittersubstantially removed.
 19. The circuit of claim 18, further comprising afrequency domain transform unit that is to produce, based on the atleast one long training symbol received at the receiver, the frequencydomain representation of the at least one long training symbol receivedat the receiver.
 20. The circuit of claim 19, further comprising adivider circuit that is to produce a channel estimate by dividing theoffset compensated frequency domain representation of the at least onelong training symbol received at the receiver by a frequency domainrepresentation of at least one long training symbol that issubstantially representative of the at least one long training symbol astransmitted by the transmitter.
 21. The circuit of claim 19, wherein thefrequency domain representation of the at least one long training symbolincludes a frequency domain representation of a first long trainingsymbol and a frequency domain representation of a second long trainingsymbol, the circuit further comprising: an averaging circuit that is toproduce an average of the frequency domain representation of the atleast one long training symbol by averaging the frequency domainrepresentation of the first long training symbol and the frequencydomain representation of the second long training symbol; wherein theconvolver is to produce the offset compensated frequency domainrepresentation of the at least one training symbol based on the averageby convolving the average of the frequency domain representation of theat least one long training symbol with the frequency domainrepresentation of the third signal; a divider circuit that is to producea channel estimate by dividing the offset compensated frequency domainrepresentation of the average with a frequency domain representation ofthe at least one long training symbol that is substantiallyrepresentative of the at least one long training symbol as transmittedby the transmitter.
 22. The circuit of claim 21, further comprising: along training symbol frequency domain representation unit that is toproduce the frequency domain representation of the at least one longtraining symbol that is substantially representative of the at least onelong training symbol as transmitted by the transmitter.
 23. The circuitof claim 20, further comprising: a second divider circuit that is todivide an offset compensated frequency domain representation of a datasymbol by the channel estimate to produce a representation of phasedifference between at least one pilot in the data symbol and at leastone pilot in the at least one long training symbol; and an average phaseoffset circuit that is to produce, based on the representation of phasedifference, an average of the phase difference between the at least onepilot in the data symbol and the at least one pilot in the at least onelong training symbol, and, based on the average of the phase difference,an updated frequency offset for application to the first signalgenerator.
 24. The circuit of claim 17 further comprising: a secondsignal generator that is to produce, based on the second vector angle, athird periodic signal; and a second mixer that is to multiply a timedomain representation of the at least one long training symbol with thethird periodic signal to produce an offset compensated time domainrepresentation of the at least one long training symbol.
 25. The circuitof claim 24, further comprising: a first frequency domain transform unitthat is to transform the offset compensated time domain representationof the at least one long training symbol to produce an offsetcompensated frequency domain representation of the at least one longtraining symbol received at the receiver; and a divider circuit that isto produce a channel estimate by dividing the offset compensatedfrequency domain representation of the at least one long training symbolreceived at the receiver by a frequency domain representation of the atleast one long training symbol that is substantially representative ofthe at least one long training symbol as transmitted by the transmitter.26. The circuit of claim 25, further comprising: a long training symbolfrequency domain representation unit that provides the frequency domainrepresentation of the at least one long training symbol that issubstantially representative of the at least one long training symbol astransmitted by the transmitter.
 27. The circuit of claim 25, furthercomprising: a second divider circuit that is to divide an offsetcompensated frequency domain representation of a data symbol by thechannel estimate to produce a representation of phase difference betweenat least one pilot in the data symbol and at least one pilot in the atleast one long training symbol received at the receiver; an averagephase offset circuit that is to produce, based on the representation ofphase difference, an average of the phase difference between the atleast one pilot in the data symbol and the at least one pilot in the atleast one long training symbol received at the receiver, and, based onthe average of the phase difference, an updated frequency offset forapplication to the first signal generator.
 28. The circuit of claim 26,further comprising: a low-pass filter that is to receive samples of theshort training symbols and produce filtered samples of the shorttraining symbols; and a summer that is to produce, by subtracting thefiltered samples of the short training symbols from the samples of theshort training symbols, short training symbol samples that have directcurrent substantially removed for application to the autocorrelator. 29.The circuit of claim 26, further comprising: a first summer that is toproduce a third vector, based on summing samples of at least one shorttraining symbol that have not been compensated for frequency offset, anda fourth vector, based on summing samples of another at least one shorttraining symbol that have not been compensated for frequency offset; adirect current offset compensator that is to receive the first vector,the third vector, and the fourth vector and is to calculate directcurrent offset by evaluating$\frac{\left( {{x1} - {x2}} \right){\mathbb{e}}^{({j\;\alpha})}}{N\left( {1 - {\mathbb{e}}^{({j\;\alpha})}} \right)}$wherein α is the first vector angle, x1 is the third vector, x2 is thefourth vector, and N is number of samples in the at least one shorttraining symbol that have not been compensated for frequency offset; anda second summer that is to produce a difference between samples ofsymbols received after the short training symbols and the direct currentoffset.
 30. The circuit of claim 26, further comprising: a first summerthat is to produce a third vector, based on summing samples of at leastone short training symbol that have not been compensated for frequencyoffset, and a fourth vector, based on summing samples of another atleast one short training symbol that have not been compensated forfrequency offset; a direct current offset compensator that is to receivethe third vector, and the fourth vector and is to calculate directcurrent offset by evaluating $\frac{\left( {{x1} - {x2}} \right)}{2N}$wherein x1 is the third vector, x2 is the fourth vector, and N is numberof samples in the at least one short training symbol that have not beencompensated for frequency offset; and a second summer that is to producea difference between samples of symbols received after the shorttraining symbols and the direct current offset.
 31. An automaticfrequency control circuit for correcting influence of frequency offsetbetween a receiver and a transmitter by evaluating training symbolsreceived during a preamble period, the circuit comprising: anautocorrelator that is to produce, based on short training symbols, afirst vector whose first vector angle is indicative of a coarse offsetbetween the receiver and the transmitter and is to produce, based on atleast one long training symbol, a second vector whose second vectorangle is indicative of a fine offset between the receiver and thetransmitter; a frequency offset generator that is to produce a coarseoffset estimate based on the first vector angle and a fine offsetestimate based on the second vector angle; a first signal generator thatis to produce, based on the coarse offset estimate, a first periodicsignal with a first frequency equivalent substantially to the coarseoffset estimate; a first mixer that is to produce a product of the atleast one long training symbol received at the receiver and the firstperiodic signal and apply the product to the autocorrelator, wherein theautocorrelator is to produce the second vector based on the product;wherein, after the fine offset estimate is produced by the frequencyoffset generator, the first signal generator is to produce a secondperiodic signal with a second frequency equivalent substantially to asum of the coarse offset estimate and the fine offset estimate; whereinthe first mixer is to multiply, with the second periodic signal, symbolsthat are received after the at least one long training symbol isreceived; an offset compensator that is produce, based on the secondvector angle, a frequency domain representation of a third signal havinga third frequency substantially equivalent to the fine offset estimate;and a convolver that is to convolve the frequency domain representationof the third signal with a frequency domain representation of the atleast one long training symbol received at the receiver to produce anoffset compensated frequency domain representation of the at least onelong training symbol that has effect of the frequency offset on channeltransfer function between the receiver and the transmitter substantiallyremoved.
 32. The circuit of claim 31, further comprising a dividercircuit that is to produce a channel estimate by dividing the offsetcompensated frequency domain representation of the at least one longtraining symbol received at the receiver by a frequency domainrepresentation of at least one long training symbol that issubstantially representative of the at least one long training symbol astransmitted by the transmitter.
 33. The circuit of claim 32, furthercomprising: a second divider circuit that is to divide an offsetcompensated frequency domain representation of a data symbol by thechannel estimate to produce a representation of phase difference betweenat least one pilot in the data symbol and at least one pilot in the atleast one long training symbol; and an average phase offset circuit thatis to produce, based on the representation of phase difference, anaverage of the phase difference between the at least one pilot in thedata symbol and the at least one pilot in the at least one long trainingsymbol, and, based on the average of the phase difference, an updatedfrequency offset for application to the first signal generator.
 34. Anautomatic frequency control circuit for correcting influence offrequency offset between a receiver and a transmitter by evaluatingtraining symbols received during a preamble period, the circuitcomprising: an autocorrelator that is to produce, based on shorttraining symbols, a first vector whose first vector angle is indicativeof a coarse offset between the receiver and the transmitter and is toproduce, based on at least one long training symbol, a second vectorwhose second vector angle is indicative of a fine offset between thereceiver and the transmitter; a frequency offset generator that is toproduce a coarse offset estimate based on the first vector angle and afine offset estimate based on the second vector angle; a first signalgenerator that is to produce, based on the coarse offset estimate, afirst periodic signal with a first frequency equivalent substantially tothe coarse offset estimate; a first mixer that is to produce a productof the at least one long training symbol received at the receiver andthe first periodic signal and apply the product to the autocorrelator,wherein the autocorrelator is to produce the second vector based on theproduct; wherein, after the fine offset estimate is produced by thefrequency offset generator, the first signal generator is to produce asecond periodic signal with a second frequency equivalent substantiallyto a sum of the coarse offset estimate and the fine offset estimate; andwherein the first mixer is to multiply, with the second periodic signal,symbols that are received after the at least one long training symbol isreceived; and a second signal generator that is to produce, based on thesecond vector angle, a third periodic signal; and a second mixer that isto multiply a time domain representation of the at least one longtraining symbol with the third periodic signal to produce an offsetcompensated time domain representation of the at least one long trainingsymbol.
 35. The circuit of claim 34, further comprising: a firstfrequency domain transform unit that is to transform the offsetcompensated time domain representation of the at least one long trainingsymbol to produce an offset compensated frequency domain representationof the at least one long training symbol received at the receiver; and adivider circuit that is to produce a channel estimate by dividing theoffset compensated frequency domain representation of the at least onelong training symbol received at the receiver by a frequency domainrepresentation of the at least one long training symbol that issubstantially representative of the at least one long training symbol astransmitted by the transmitter.
 36. The circuit of claim 35, furthercomprising: a second divider circuit that is to divide an offsetcompensated frequency domain representation of a data symbol by thechannel estimate to produce a representation of phase difference betweenat least one pilot in the data symbol and at least one pilot in the atleast one long training symbol received at the receiver; an averagephase offset circuit that is to produce, based on the representation ofphase difference, an average of the phase difference between the atleast one pilot in the data symbol and the at least one pilot in the atleast one long training symbol received at the receiver, and, based onthe average of the phase difference, an updated frequency offset forapplication to the first signal generator.
 37. An automatic frequencycontrol circuit for correcting influence of frequency offset between areceiver and a transmitter by evaluating training symbols receivedduring a preamble period, the circuit comprising: an autocorrelator thatis to produce, based on short training symbols, a first vector whosefirst vector angle is indicative of a coarse offset between the receiverand the transmitter and is to produce, based on at least one longtraining symbol, a second vector whose second vector angle is indicativeof a fine offset between the receiver and the transmitter; a frequencyoffset generator that is to produce a coarse offset estimate based onthe first vector angle and a fine offset estimate based on the secondvector angle; a first signal generator that is to produce, based on thecoarse offset estimate, a first periodic signal with a first frequencyequivalent substantially to the coarse offset estimate; a first mixerthat is to produce a product of the at least one long training symbolreceived at the receiver and the first periodic signal and apply theproduct to the autocorrelator, wherein the autocorrelator is to producethe second vector based on the product; wherein, after the fine offsetestimate is produced by the frequency offset generator, the first signalgenerator is to produce a second periodic signal with a second frequencyequivalent substantially to a sum of the coarse offset estimate and thefine offset estimate; wherein the first mixer is to multiply, with thesecond periodic signal, symbols that are received after the at least onelong training symbol is received; a low-pass filter that is to receivesamples of the short training symbols and produce filtered samples ofthe short training symbols; and a summer that is to produce, bysubtracting the filtered samples of the short training symbols from thesamples of the short training symbols, short training symbol samplesthat have direct current substantially removed for application to theautocorrelator.
 38. An automatic frequency control circuit forcorrecting influence of frequency offset between a receiver and atransmitter by evaluating training symbols received during a preambleperiod, the circuit comprising: an autocorrelator that is to produce,based on short training symbols, a first vector whose first vector angleis indicative of a coarse offset between the receiver and thetransmitter and is to produce, based on at least one long trainingsymbol, a second vector whose second vector angle is indicative of afine offset between the receiver and the transmitter; a frequency offsetgenerator that is to produce a coarse offset estimate based on the firstvector angle and a fine offset estimate based on the second vectorangle; a first signal generator that is to produce, based on the coarseoffset estimate, a first periodic signal with a first frequencyequivalent substantially to the coarse offset estimate; a first mixerthat is to produce a product of the at least one long training symbolreceived at the receiver and the first periodic signal and apply theproduct to the autocorrelator, wherein the autocorrelator is to producethe second vector based on the product; wherein, after the fine offsetestimate is produced by the frequency offset generator, the first signalgenerator is to produce a second periodic signal with a second frequencybased on the coarse offset estimate and the fine offset estimate;wherein the first mixer is to multiply, with the second periodic signal,symbols that are received after the at least one long training symbol isreceived; a first summer that is to produce a third vector, based onsumming samples of at least one short training symbol that have not beencompensated for frequency offset, and a fourth vector, based on summingsamples of another at least one short training symbol that have not beencompensated for frequency offset; a direct current offset compensatorthat is to receive the first vector, the third vector, and the fourthvector and is to calculate direct current offset by evaluating$\frac{\left( {{x1} - {x2}} \right){\mathbb{e}}^{({j\;\alpha})}}{N\left( {1 - {\mathbb{e}}^{({j\;\alpha})}} \right)}$wherein α is the first vector angle, x1 is the third vector, x2 is thefourth vector, and N is number of samples in the at least one shorttraining symbol that have not been compensated for frequency offset; anda second summer that is to produce a difference between samples ofsymbols received after the short training symbols and the direct currentoffset.
 39. An automatic frequency control circuit for correctinginfluence of frequency offset between a receiver and a transmitter byevaluating training symbols received during a preamble period, thecircuit comprising: an autocorrelator that is to produce, based on shorttraining symbols, a first vector whose first vector angle is indicativeof a coarse offset between the receiver and the transmitter and is toproduce, based on at least one long training symbol, a second vectorwhose second vector angle is indicative of a fine offset between thereceiver and the transmitter; a frequency offset generator that is toproduce a coarse offset estimate based on the first vector angle and afine offset estimate based on the second vector angle; a first signalgenerator that is to produce, based on the coarse offset estimate, afirst periodic signal with a first frequency equivalent substantially tothe coarse offset estimate; a first mixer that is to produce a productof the at least one long training symbol received at the receiver andthe first periodic signal and apply the product to the autocorrelator,wherein the autocorrelator is to produce the second vector based on theproduct; wherein, after the fine offset estimate is produced by thefrequency offset generator, the first signal generator is to produce asecond periodic signal with a second frequency equivalent substantiallyto a sum of the coarse offset estimate and the fine offset estimate;wherein the first mixer is to multiply, with the second periodic signal,symbols that are received after the at least one long training symbol isreceived; a first summer that is to produce a third vector, based onsumming samples of at least one short training symbol that have not beencompensated for frequency offset, and a fourth vector, based on summingsamples of another at least one short training symbol that have not beencompensated for frequency offset; a direct current offset compensatorthat is to receive the third vector, and the fourth vector and is tocalculate direct current offset by evaluating$\frac{\left( {{x1} + {x2}} \right)}{2N}$ wherein x1 is the thirdvector, x2 is the fourth vector, and N is number of samples in the atleast one short training symbol that have not been compensated forfrequency offset; and a second summer that is to produce a differencebetween samples of symbols received after the short training symbols andthe direct current offset.
 40. A method for correcting influence offrequency offset between a receiver and a transmitter by evaluatingtraining symbols received during a preamble period, the methodcomprising: producing, based on short training symbols, a first vectorwhose first vector angle is indicative of a coarse offset between thereceiver and the transmitter and, based on at least one long trainingsymbol, a second vector whose second vector angle is indicative of afine offset between the receiver and the transmitter; producing a coarseoffset estimate based on the first vector angle and a fine offsetestimate based on the second vector angle; producing based on the coarseoffset estimate, a first periodic signal with a first frequencyequivalent substantially to the coarse offset estimate; producing aproduct of the at least one long training symbol received at thereceiver and the first periodic signal and apply the product to anautocorrelator, wherein the autocorrelator is to produce the secondvector based on the product; generating, after the fine offset estimateis produced, a second periodic signal with a second frequency based onthe coarse offset estimate and the fine offset estimate; andmultiplying, with the second periodic signal, symbols that are receivedafter the at least one long training symbol is received.
 41. The methodof claim 40, further comprising: producing, based on the second vectorangle, a frequency domain representation of a third signal having athird frequency substantially equivalent to the fine offset estimate;and convolving the frequency domain representation of the third signalwith a frequency domain representation of the at least one long trainingsymbol received at the receiver to produce an offset compensatedfrequency domain representation of the at least one long training symbolthat has effect of the frequency offset between the receiver and thetransmitter substantially removed.
 42. The method of claim 41,producing, based on the at least one long training symbol received atthe receiver, the frequency domain representation of the at least onelong training symbol received at the receiver.
 43. The method of claim42, further comprising producing a channel estimate by dividing theoffset compensated frequency domain representation of the at least onelong training symbol received at the receiver by a frequency domainrepresentation of at least one long training symbol that issubstantially representative of the at least one long training symbol astransmitted by the transmitter.
 44. The method of claim 42, wherein thefrequency domain representation of the at least one long training symbolincludes a frequency domain representation of a first long trainingsymbol and a frequency domain representation of a second long trainingsymbol, the method further comprising: producing an average of thefrequency domain representation of the at least one long training symbolby averaging the frequency domain representation of the first longtraining symbol and the frequency domain representation of the secondlong training symbol; producing the offset compensated frequency domainrepresentation of the at least one training symbol based on the averageby convolving the average of the frequency domain representation of theat least one long training symbol with the frequency domainrepresentation of the third signal; producing a channel estimate bydividing the offset compensated frequency domain representation of theaverage with a frequency domain representation of the at least one longtraining symbol that is substantially representative of the at least onelong training symbol as transmitted by the transmitter.
 45. The methodof claim 44, further comprising: producing the frequency domainrepresentation of the at least one long training symbol that issubstantially representative of the at least one long training symbol astransmitted by the transmitter.
 46. The method of claim 43, furthercomprising: dividing an offset compensated frequency domainrepresentation of a data symbol by the channel estimate to produce arepresentation of phase difference between at least one pilot in thedata symbol and at least one pilot in the at least one long trainingsymbol; and producing, based on the representation of phase difference,an average of the phase difference between the at least one pilot in thedata symbol and the at least one pilot in the at least one long trainingsymbol, and, based on the average of the phase difference, an updatedfrequency offset for application to a first signal generator.
 47. Themethod of claim 43, further comprising: providing an offset compensatedfrequency domain representation of a first data symbol and an offsetcompensated frequency domain representation of a second data symbol;dividing the offset compensated frequency domain representation of thefirst data symbol by the offset compensated frequency domainrepresentation of the second data symbol to produce a representation ofphase difference between at least one pilot in the first data symbol andat least one pilot in the second data symbol; and producing, based onthe representation of phase difference, an average of the phasedifference between the at least one pilot in the first data symbol andthe at least one pilot in the second data symbol, and, based on theaverage of the phase difference, an updated frequency offset forapplication to a first signal generator.
 48. The method of claim 40,further comprising: producing, based on the second vector angle, a thirdperiodic signal; and multiplying a time domain representation of the atleast one long training symbol with the third periodic signal to producean offset compensated time domain representation of the at least onelong training symbol.
 49. The method of claim 48, further comprising:transforming the offset compensated time domain representation of the atleast one long training symbol to produce an offset compensatedfrequency domain representation of the at least one long training symbolreceived at the receiver; and producing a channel estimate by dividingthe offset compensated frequency domain representation of the at leastone long training symbol received at the receiver by a frequency domainrepresentation of the at least one long training symbol that issubstantially representative of the at least one long training symbol astransmitted by the transmitter.
 50. The method of claim 49, furthercomprising: providing the frequency domain representation of the atleast one long training symbol that is substantially representative ofthe at least one long training symbol as transmitted by the transmitter.51. The method of claim 49, further comprising: dividing an offsetcompensated frequency domain representation of a data symbol by thechannel estimate to produce a representation of phase difference betweenat least one pilot in the data symbol and at least one pilot in the atleast one long training symbol received at the receiver; producing,based on the representation of phase difference, an average of the phasedifference between the at least one pilot in the data symbol and the atleast one pilot in the at least one long training symbol received at thereceiver, and, based on the average of the phase difference, an updatedfrequency offset for application to a first signal generator.
 52. Themethod of claim 49, further comprising: providing an offset compensatedfrequency domain representation of a first data symbol and an offsetcompensated frequency domain representation of a second data symbol;dividing the offset compensated frequency domain representation of thefirst data symbol by the offset compensated frequency domainrepresentation of the second data symbol to produce a representation ofphase difference between at least one pilot in the first data symbol andat least one pilot in the second data symbol; and producing, based onthe representation of phase difference, an average of the phasedifference between the at least one pilot in the first data symbol andthe at least one pilot in the second data symbol, and, based on theaverage of the phase difference, an updated frequency offset.
 53. Themethod of claim 40, further comprising: receiving samples of the shorttraining symbols; producing filtered samples of the short trainingsymbols based on the received samples of the short training symbols; andsubtracting the filtered samples of the short training symbols from thesamples of the short training symbols to produce short training symbolsamples that have direct current substantially removed.
 54. The methodof claim 40, further comprising: producing a third vector, based onsumming samples of at least one short training symbol that have not beencompensated for frequency offset, and a fourth vector, based on summingsamples of another at least one short training symbol that have not beencompensated for frequency offset; calculating a direct current offset byevaluating$\frac{\left( {{x1} - {x2}} \right){\mathbb{e}}^{({j\;\alpha})}}{N\left( {1 - {\mathbb{e}}^{({j\;\alpha})}} \right)}$wherein α is the first vector angle, x1 is the third vector, x2 is thefourth vector, and N is number of samples in the at least one shorttraining symbol that have not been compensated for frequency offset; andproducing a difference between samples of symbols received after theshort training symbols and the direct current offset.
 55. The method ofclaim 40, further comprising: producing a third vector, based on summingsamples of at least one short training symbol that have not beencompensated for frequency offset, and a fourth vector, based on summingsamples of another at least one short training symbol that have not beencompensated for frequency offset; calculating a direct current offset byevaluating $\frac{\left( {{x1} + {x2}} \right)}{2N}$ wherein x1 is thethird vector, x2 is the fourth vector, and N is number of samples in theat least one short training symbol that have not been compensated forfrequency offset; and producing a difference between samples of symbolsreceived after the short training symbols and the direct current offset.56. A method for correcting influence of frequency offset between areceiver and a transmitter by evaluating training symbols receivedduring a preamble period, the method comprising: producing, based onshort training symbols, a first vector whose first vector angle isindicative of a coarse offset between the receiver and the transmitterand is to produce, based on at least one long training symbol, a secondvector whose second vector angle is indicative of a fine offset betweenthe receiver and the transmitter; producing a coarse offset estimatebased on the first vector angle and a fine offset estimate based on thesecond vector angle; producing based on the coarse offset estimate, afirst periodic signal with a first frequency equivalent substantially tothe coarse offset estimate; producing a product of the at least one longtraining symbol received at the receiver and the first periodic signaland apply the product to an autocorrelator, wherein the autocorrelatoris to produce the second vector based on the product; generating, afterthe fine offset estimate is produced, a second periodic signal with asecond frequency equivalent substantially to a sum of the coarse offsetestimate and the fine offset estimate; multiplying, with the secondperiodic signal, symbols that are received after the at least one longtraining symbol is received; producing, based on the second vectorangle, a frequency domain representation of a third signal having athird frequency substantially equivalent to the fine offset estimate;and convolving the frequency domain representation of the third signalwith a frequency domain representation of the at least one long trainingsymbol received at the receiver to produce an offset compensatedfrequency domain representation of the at least one long training symbolthat has effect of the frequency offset on channel transfer functionbetween the receiver and the transmitter substantially removed.
 57. Themethod of claim 56, further comprising producing a channel estimate bydividing the offset compensated frequency domain representation of theat least one long training symbol received at the receiver by afrequency domain representation of at least one long training symbolthat is substantially representative of the at least one long trainingsymbol as transmitted by the transmitter.
 58. The method of claim 57,further comprising: dividing an offset compensated frequency domainrepresentation of a data symbol by the channel estimate to produce arepresentation of phase difference between at least one pilot in thedata symbol and at least one pilot in the at least one long trainingsymbol; and producing, based on the representation of phase difference,an average of the phase difference between the at least one pilot in thedata symbol and the at least one pilot in the at least one long trainingsymbol, and, based on the average of the phase difference, an updatedfrequency offset for application to a first signal generator.
 59. Themethod of claim 57, further comprising: providing an offset compensatedfrequency domain representation of a first data symbol and an offsetcompensated frequency domain representation of a second data symbol;dividing the offset compensated frequency domain representation of thefirst data symbol by the offset compensated frequency domainrepresentation of the second data symbol to produce a representation ofphase difference between at least one pilot in the first data symbol andat least one pilot in the second data symbol; and producing, based onthe representation of phase difference, an average of the phasedifference between the at least one pilot in the first data symbol andthe at least one pilot in the second data symbol, and, based on theaverage of the phase difference, an updated frequency offset forapplication to a first signal generator.
 60. The method of claim 57,wherein the frequency domain representation of the at least one longtraining symbol includes a frequency domain representation of a firstlong training symbol and a frequency domain representation of a secondlong training symbol, the method further comprising: producing anaverage of the frequency domain representation of the at least one longtraining symbol by averaging the frequency domain representation of thefirst long training symbol and the frequency domain representation ofthe second long training symbol; producing offset compensated frequencydomain representation of the at least one training symbol based on theaverage by convolving the average of the frequency domain representationof the at least one long training symbol with the frequency domainrepresentation of the third signal; producing the channel estimate bydividing the offset compensated frequency domain representation of theaverage with a frequency domain representation of the at least one longtraining symbol that is substantially representative of the at least onelong training symbol as transmitted by the transmitter.
 61. A method forcorrecting influence of frequency offset between a receiver and atransmitter by evaluating training symbols received during a preambleperiod, the method comprising: producing, based on short trainingsymbols, a first vector whose first vector angle is indicative of acoarse offset between the receiver and the transmitter and is toproduce, based on at least one long training symbol, a second vectorwhose second vector angle is indicative of a fine offset between thereceiver and the transmitter; producing a coarse offset estimate basedon the first vector angle and a fine offset estimate based on the secondvector angle; producing based on the coarse offset estimate, a firstperiodic signal with a first frequency equivalent substantially to thecoarse offset estimate; producing a product of the at least one longtraining symbol received at the receiver and the first periodic signaland apply the product to an autocorrelator, wherein the autocorrelatoris to produce the second vector based on the product; generating, afterthe fine offset estimate is produced, a second periodic signal with asecond frequency equivalent substantially to a sum of the coarse offsetestimate and the fine offset estimate; multiplying, with the secondperiodic signal, symbols that are received after the at least one longtraining symbol is received; producing, based on the second vectorangle, a third periodic signal; and multiplying a time domainrepresentation of the at least one long training symbol with the thirdperiodic signal to produce an offset compensated time domainrepresentation of the at least one long training symbol.
 62. The methodof claim 61, further comprising: transforming the offset compensatedtime domain representation of the at least one long training symbol toproduce an offset compensated frequency domain representation of the atleast one long training symbol received at the receiver; and producing achannel estimate by dividing the offset compensated frequency domainrepresentation of the at least one long training symbol received at thereceiver by a frequency domain representation of the at least one longtraining symbol that is substantially representative of the at least onelong training symbol as transmitted by the transmitter.
 63. The methodof claim 62, further comprising: dividing an offset compensatedfrequency domain representation of a data symbol by the channel estimateto produce a representation of phase difference between at least onepilot in the data symbol and at least one pilot in the at least one longtraining symbol received at the receiver; producing, based on therepresentation of phase difference, an average of the phase differencebetween the at least one pilot in the data symbol and the at least onepilot in the at least one long training symbol received at the receiver,and, based on the average of the phase difference, an updated frequencyoffset for application to a first signal generator.
 64. The method ofclaim 62, further comprising: providing an offset compensated frequencydomain representation of a first data symbol and an offset compensatedfrequency domain representation of a second data symbol; dividing theoffset compensated frequency domain representation of the first datasymbol by the offset compensated frequency domain representation of thesecond data symbol to produce a representation of phase differencebetween at least one pilot in the first data symbol and at least onepilot in the second data symbol; and producing, based on therepresentation of phase difference, an average of the phase differencebetween the at least one pilot in the first data symbol and the at leastone pilot in the second data symbol, and, based on the average of thephase difference, an updated frequency offset.
 65. An automaticfrequency control circuit for correcting influence of frequency offsetbetween a receiver and a transmitter by evaluating training symbolsreceived during a preamble period, the circuit comprising: anautocorrelator that is to produce, based on short training symbols, afirst vector whose first vector angle is indicative of a coarse offsetbetween the receiver and the transmitter and is to produce, based on atleast one long training symbol, a second vector whose second vectorangle is indicative of a fine offset between the receiver and thetransmitter; a frequency offset generator that is to produce a coarseoffset estimate based on the first vector angle and a fine offsetestimate based on the second vector angle; a first signal generator thatis to produce, based on the coarse offset estimate, a first periodicsignal with a first frequency equivalent substantially to the coarseoffset estimate; a first mixer that is to produce a product of the atleast one long training symbol received at the receiver and the firstperiodic signal and apply the product to the autocorrelator, wherein theautocorrelator is to produce the second vector based on the product;wherein, after the fine offset estimate is produced by the frequencyoffset generator, the first signal generator is to produce a secondperiodic signal with a second frequency equivalent substantially to asum of the coarse offset estimate and the fine offset estimate; whereinthe first mixer is to multiply, with the second periodic signal, symbolsthat are received after the at least one long training symbol isreceived; receiving samples of the short training symbols; producingfiltered samples of the short training symbols based on the receivedsamples of the short training symbols; and subtracting the filteredsamples of the short training symbols from the samples of the shorttraining symbols to produce short training symbol samples that havedirect current substantially removed.
 66. An automatic frequency controlcircuit for correcting influence of frequency offset between a receiverand a transmitter by evaluating training symbols received during apreamble period, the circuit comprising: an autocorrelator that is toproduce, based on short training symbols, a first vector whose firstvector angle is indicative of a coarse offset between the receiver andthe transmitter and is to produce, based on at least one long trainingsymbol, a second vector whose second vector angle is indicative of afine offset between the receiver and the transmitter; a frequency offsetgenerator that is to produce a coarse offset estimate based on the firstvector angle and a fine offset estimate based on the second vectorangle; a first signal generator that is to produce, based on the coarseoffset estimate, a first periodic signal with a first frequencyequivalent substantially to the coarse offset estimate; a first mixerthat is to produce a product of the at least one long training symbolreceived at the receiver and the first periodic signal and apply theproduct to the autocorrelator, wherein the autocorrelator is to producethe second vector based on the product; wherein, after the fine offsetestimate is produced by the frequency offset generator, the first signalgenerator is to produce a second periodic signal with a second frequencyequivalent substantially to a sum of the coarse offset estimate and thefine offset estimate; wherein the first mixer is to multiply, with thesecond periodic signal, symbols that are received after the at least onelong training symbol is received; producing a third vector, based onsumming samples of at least one short training symbol that have not beencompensated for frequency offset, and a fourth vector, based on summingsamples of another at least one short training symbol that have not beencompensated for frequency offset; calculating a direct current offset byevaluating$\frac{\left( {{x1} - {x2}} \right){\mathbb{e}}^{({j\alpha})}}{N\left( {1 - {\mathbb{e}}^{({j\alpha})}} \right)}$wherein α is the first vector angle, x1 is the third vector, x2 is thefourth vector, and N is number of samples in the at least one shorttraining symbol that have not been compensated for frequency offset; andproducing a difference between samples of symbols received after theshort training symbols and the direct current offset.
 67. An automaticfrequency control circuit for correcting influence of frequency offsetbetween a receiver and a transmitter by evaluating training symbolsreceived during a preamble period, the circuit comprising: anautocorrelator that is to produce, based on short training symbols, afirst vector whose first vector angle is indicative of a coarse offsetbetween the receiver and the transmitter and is to produce, based on atleast one long training symbol, a second vector whose second vectorangle is indicative of a fine offset between the receiver and thetransmitter; a frequency offset generator that is to produce a coarseoffset estimate based on the first vector angle and a fine offsetestimate based on the second vector angle; a first signal generator thatis to produce, based on the coarse offset estimate, a first periodicsignal with a first frequency equivalent substantially to the coarseoffset estimate; a first mixer that is to produce a product of the atleast one long training symbol received at the receiver and the firstperiodic signal and apply the product to the autocorrelator, wherein theautocorrelator is to produce the second vector based on the product;wherein, after the fine offset estimate is produced by the frequencyoffset generator, the first signal generator is to produce a secondperiodic signal with a second frequency equivalent substantially to asum of the coarse offset estimate and the fine offset estimate; whereinthe first mixer is to multiply, with the second periodic signal, symbolsthat are received after the at least one long training symbol isreceived; producing a third vector, based on summing samples of at leastone short training symbol that have not been compensated for frequencyoffset, and a fourth vector, based on sunning samples of another atleast one short training symbol that have not been compensated forfrequency offset; calculating a direct current offset by evaluating$\frac{\left( {{x1} + {x2}} \right)}{2N}$ wherein x1 is the thirdvector, x2 is the fourth vector, and N is number of samples in the atleast one short training symbol that have not been compensated forfrequency offset; and producing a difference between samples of symbolsreceived after the short training symbols and the direct current offset.